Question

A major car manufacturing firm issues a 20 year $1,000,000 bond at par. The bond pays a 6% (APR) semiannual coupon. 5 years later, the Federal Reserve Board cuts the fed funds rate, causing interest rates for similar firms to fall to 4% (APR). What is the new bond price? (a) $1,222,368 (b) $1,223,965 (c) $1,000,000 (d) $1,273,555 . If you bought the bond at issue and held it to maturity, what is the effective annual rate (EAR) that you earned? (a) 6% (b) 6.09% (c) 4%

Answer 1

A1	B	C	D	E	F	G	H	I	J	K
2
3
4		Par value (F)	$1,000,000
5		Interest rate (Coupon rate)	6.00%
6		Market demanded return (Yield to maturity)	4.00%
7		Time to maturity	15	Years
8
9		Interest is paid twice a year i.e. semiannual.
10		Semiannual coupon (C)	$30,000.00
11		Semiannual Period (n)	30
12		Semiannual YTM (i)	2.00%
13		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
14		Cash Flow of Bonds can be written as follows:
15		Semiannual Period	0	1	2	3	4	…	30
16		Cash Flow of Bonds		$30,000	$30,000	$30,000	$30,000	$30,000	$1,030,000
17
18		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
19		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
20
21		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
22			=40*(P/A,3%,10)+1,000*(P/F,3%,10)
23			$1,223,964.56	=D10*PV(D12,D11,-1,0)+D4*(1/((1+D12)^D11))
24		Hence current market value of bond is	$1,223,965
25
26		Alternative method:
27		Price of the bond can also be calculated by finding the present value of cash flows of the bond using PV formula of excel as follows:
28		RATE	2.00%
29		NPER	30
30		PMT	$30,000.00
31		FV	$1,000,000
32		TYPE	0	(End of the period Cash Flow)
33
34		Price of the Bond	$1,223,965	=-PV(D28,D29,D30,D31,0)
35
36		Hence Bond Price is	$1,223,965
37		Thus the option (c) is correct.
38
39		Since the bond is issued at par therefore the yield to maturity will be equal to the coupon rate.
40		Yield to maturity	6%
41
42		Since Compounding is Semiannual, therefore the EAR can be calculated as follows:
43
44		Effective annual rate	=((1+APR/m)^m)-1
45
46		Where APR is annual percentage rate quoted, m is compounding factor.
47
48		Effective interest rate being charged by bank can be calculated as follows:
49		APR	6.00%
50		m	2	(for Semi-annual compounding)
51
52		Effective annual rate	=((1+APR/m)^m)-1
53			6.09%	=((1+D49/D50)^D50)-1
54
55		Hence EAR is	6.09%
56		Thus the option (b) is correct.
57